Wireless Communication Device and Corresponding Apparatus, Method and Computer Program

ABSTRACT

Embodiments of the present disclosure relate to wireless communication devices, systems comprising wireless communication devices, and to an apparatus, a method and a computer program for a wireless communication device. The apparatus comprises a transceiver module for transmitting and receiving wireless transmissions. The apparatus comprises a processing module that is configured to control the transceiver module. The processing module is configured to communicate with a further wireless communication device via the transceiver module. The communication with the further wireless communication device is based on a transmission of data frames between the wireless communication device and the further wireless communication device. Each data frame is based on a two-dimensional grid in a time-frequency plane having a time dimension resolution and a frequency dimension resolution. The two-dimensional time-frequency grid is derived from a two-dimensional grid in a delay-Doppler plane having a delay dimension and a Doppler dimension. The processing module is configured to perform equalization on received data frames. The equalization is performed using a minimum mean square equalizer. The minimum mean square equalizer comprises a term to compensate for self-interference.

Embodiments of the present disclosure relate to wireless communicationdevices, systems comprising wireless communication devices, and to anapparatus, a method and a computer program for a wireless communicationdevice.

New requirements in terms of reliability and efficiency in high mobilityenvironments, such as vehicle-to-vehicle (V2V) communication, arepushing legacy systems to their limits. Orthogonal frequency-divisionmultiplexing (OFDM) is a popular and well-known modulation scheme but itmay suffer from substantial performance degradation and inflexibility inenvironments with high Doppler spreads. Consequently, novel modulationschemes may be considered and perused which are flexible, efficient androbust in doubly-dispersive channels.

Orthogonal time frequency and space (OTFS) was introduced by Hadani et.al as a promising recent combination of classical pulse-shapedWeyl-Heisenberg (or Gabor) multicarrier schemes with a distincttime-frequency (TF) spreading. Data symbols are spread with thesymplectic finite Fourier transform (SFFT) over the whole time-frequencygrid. This particular linear pre-coding accounts for thedoubly-dispersive nature of time-varying multipath channels seen aslinear combinations of time-frequency shifts. Several studies show thatOTFS outperforms OFDM in such situations. Other research focus on aperformance comparison of OFDM, generalized frequency divisionmultiplexing (GFDM), and OTFS. It reveals significant advantages of OTFSin terms of bit error rate (BER) and frame error rate (FER) in relationto the others. With sufficient accurate channel information it offers apromising increase in terms of reliability and robustness for highmobility users when using sophisticated equalizers. So far, OTFS wasresearched with the assumption of perfect grid-matching, often withidealized pulses violating the uncertainty principle and in many caseswith ideal channel knowledge (including the cross-talk channelcoefficients).

There may be a desire for providing an improved concept for the use ofOTFS or OTFS-like modulation in real-world scenarios.

This desire is addressed by the subject-matter of the independentclaims.

Embodiments are based on the finding that, in the discussion of OTFS inliterature, perfect grid matching was assumed. To fully exploitdiversity in OTFS, the 2D-deconvolution implemented by a linearequalizer should approximately invert the doubly-dispersive channeloperation, which however is a twisted convolution. In theory this isachieved by choosing the time-frequency grid and the Gabor synthesis andanalysis pulses based on the delay and Doppler spread of the channel.However, in practice a balance may be struck between supporting highgranularity in delay-Doppler spread and multi-user and network aspects.

In particular, at the receiver, computationally feasible equalizers(such as minimum mean square equalizers) suffer from the mismatchedtime-frequency grids. This may be avoided if the grid that is used forcommunicating is matched to the Gabor synthesis and analysis pulsesbased on the delay and Doppler spread of the channel. Embodiments mayperform equalization that takes into account the self-interferenceincurred on the channel, which may enable a use of a computationallyfeasible equalizer, like the minimum mean square equalizer. In order tokeep the complexity low, the grid may be chosen from a pre-defined setof “mobility modes”, which may define the dimensions of the grid, andoptionally, the shape of the pulses used.

Embodiments of the present disclosure provide an apparatus for awireless communication device. The apparatus comprises a transceivermodule for transmitting and receiving wireless transmissions. Theapparatus comprises a processing module that is configured to controlthe transceiver module. The processing module is configured tocommunicate with a further wireless communication device via thetransceiver module. The communication with the further wirelesscommunication device is based on a transmission of data frames betweenthe wireless communication device and the further wireless communicationdevice. Each data frame is based on a two-dimensional grid in atime-frequency plane having a time dimension resolution and a frequencydimension resolution. The two-dimensional time-frequency grid is derivedfrom a two-dimensional grid in a delay-Doppler plane having a delaydimension and a Doppler dimension. The processing module is configuredto perform equalization on received data frames. The equalization isperformed using a minimum mean square equalizer. The minimum mean squareequalizer comprises a term to compensate for self-interference. Byincluding a term to compensate for self-interference, the use of a morecomplex maximum likelihood estimator may be avoided while providingsufficiently good equalization.

In various embodiments, the processing module may be configured todetermine the term to compensate for self-interference using apreviously received data frame. For example, the previously receiveddata frame may be used to determine a spreading function of the channel,which may, in turn, be used to determine the term to compensate forself-interference.

In some embodiments, the processing module may be configured todetermine the term to compensate self-interference by performing theequalization using a plurality of values for the term to compensate forself-interference, evaluating a quality of a result of the equalizationperformed using the plurality of values, and selecting a value of theplurality of values for the term to compensate for self-interferencebased on the evaluation. For example, multiple values may be evaluatedand the best value may be chosen.

For example, each data frame may comprise a pilot symbol and a pluralityof guard symbols surrounding the pilot symbol. The processing module maybe configured to determine the term to compensate for self-interferenceusing the guard symbol and a subset of the plurality of guard symbols ofthe previously received data frame. Using the guard and pilot symbols,the self-interference may be estimated, and an appropriate compensationterm may be chosen. In other words, the term to compensate forself-interference may be chosen such, that, if applied to the receiveddata frame, the self-interference that is perceivable in the guardsymbols is reduced (compared to other values for the term to compensatefor self-interference). This may enable a selection of the term tocompensate for self-interference by observing its effects on theself-interference perceivable in the guard symbols.

For example, the two-dimensional time-frequency grid may be derived froma two-dimensional grid in a delay-Doppler plane having a delay dimensionand a Doppler dimension. The processing module may be configured toperform a symplectic Fourier transform on the received data frame. Thesymplectic Fourier transform may be performed (only) for the points onthe two-dimensional grid in the delay-Doppler plane corresponding topilot symbol and to the subset of the plurality of guard symbols. Theprocessing module may be configured to determine the term to compensatefor self-interference based on a result of the symplectic Fouriertransform. For example, if the guard symbols have a pre-defined value(e.g. zero), the delay spread and Doppler spread of the pilot symbol maybe seen in the values obtained for the guard symbols. The term tocompensate for self-interference may be chosen such, that the delayspread and Doppler spread of the pilot symbol perceived in the guardsymbols is reduced (compared to other values for the term to compensatefor self-interference).

In some embodiments, the processing module may be configured toperiodically update the term to compensate for the self-interference.For example, the term to compensate for the self-interference may beupdated every few frames (since the channel often does not change tooquickly). By periodically updating the term to compensate for theself-interference, the term may be adjusted to the present channelbetween the wireless communication devices.

Alternatively or additionally, the processing module may be configuredto update the term to compensate for the self-interference if abit-error rate of a received data frame exceeds a threshold. Forexample, this may lead to an update of the term to compensate for theself-interference when the channel changes, which may be less frequentthan the periodic update.

The processing module may be configured to select a communication modefrom a plurality of communication modes for the communication betweenthe wireless communication device and the wireless communication device.The communication mode may define a combination of a frequency dimensionresolution and a time dimension resolution of the two-dimensional gridin the time-frequency plane. By selecting one of a plurality ofcommunication modes, a communication mode can be chosen for thecommunication between the wireless communication device and the wirelesscommunication device that suits the channel and/or the relative velocityof the wireless communication devices, which may have a major impact onthe self-interference perceived by the receiver.

In some embodiments, the processing module is configured to select thecommunication mode from the plurality of communication modes based on anestimated self-interference of the plurality of communication modes. Theself-interference may, for example, indicate a delay spread and/or aDoppler-spread of a channel used for the communication. By using theself-interference as a criterion, an appropriate communication mode maybe selected. For example, a communication mode having a higherresolution in the frequency dimension may be appropriate for channelswith a larger delay spread, and a communication mode having a higherresolution in the time dimension may be appropriate for channels with alarger Doppler spread.

In some embodiments, the data frame is an Orthogonal Time-FrequencySpreading data frame. For example, the proposed equalization may be usedfor OTFS data frames.

Embodiments further provide a wireless communication device comprisingthe apparatus.

Embodiments further provide a system comprising a wireless communicationdevice and a further wireless communication device. The wirelesscommunication device and the further wireless communication device eachcomprise the apparatus. The wireless communication device and thefurther wireless communication device are configured to communicate witheach other.

Embodiments of the present disclosure further provide a method for awireless communication device. The method comprises communicating with afurther wireless communication device. The communication with thefurther wireless communication device is based on a transmission of dataframes between the wireless communication device and the furtherwireless communication device. Each data frame is based on atwo-dimensional grid in a time-frequency plane having a time dimensionresolution and a frequency dimension resolution. The two-dimensionaltime-frequency grid is derived from a two-dimensional grid in adelay-Doppler plane having a delay dimension and a Doppler dimension.The method comprises performing equalization on received data frames,wherein the equalization is performed using a minimum mean squareequalizer. The minimum mean square equalizer comprises a term tocompensate for self-interference.

In some embodiments, the method comprises selecting a communication modefrom a plurality of communication modes for the communication betweenthe wireless communication device and the wireless communication device.The communication mode defines a combination of a frequency dimensionresolution and a time dimension resolution of the two-dimensional gridin the time-frequency plane.

Embodiments of the present disclosure provide a computer program havinga program code for performing the method, when the computer program isexecuted on a computer, a processor, or a programmable hardwarecomponent.

Some examples of apparatuses and/or methods will be described in thefollowing by way of example only, and with reference to the accompanyingfigures, in which

FIG. 1 shows an exemplary OTFS frame;

FIG. 2a shows a block diagram of an embodiment of an apparatus for awireless communication device and of a wireless communication device;

FIG. 2b shows a block diagram of an embodiment of a system;

FIGS. 2c and 2d show flow charts of embodiments of a method for awireless communication device;

FIGS. 3a and 3b depict Signal-to-Noise-Ratio required to attain adesired bit-error rate in an evaluation of an embodiment;

FIG. 3c summarizes parameters used to obtain the numerical results ofFIGS. 3a and 3b ; and

FIGS. 4a to 4d show bit-error rate curves for three distinct vehicularchannels for different mobility modes.

Various examples will now be described more fully with reference to theaccompanying drawings in which some examples are illustrated. In thefigures, the thicknesses of lines, layers and/or regions may beexaggerated for clarity.

Accordingly, while further examples are capable of various modificationsand alternative forms, some particular examples thereof are shown in thefigures and will subsequently be described in detail. However, thisdetailed description does not limit further examples to the particularforms described. Further examples may cover all modifications,equivalents, and alternatives falling within the scope of thedisclosure. Same or like numbers refer to like or similar elementsthroughout the description of the figures, which may be implementedidentically or in modified form when compared to one another whileproviding for the same or a similar functionality.

It will be understood that when an element is referred to as being“connected” or “coupled” to another element, the elements may bedirectly connected or coupled via one or more intervening elements. Iftwo elements A and B are combined using an “or”, this is to beunderstood to disclose all possible combinations, i.e. only A, only B aswell as A and B, if not explicitly or implicitly defined otherwise. Analternative wording for the same combinations is “at least one of A andB” or “A and/or B”. The same applies, mutatis mutandis, for combinationsof more than two Elements.

The terminology used herein for the purpose of describing particularexamples is not intended to be limiting for further examples. Whenever asingular form such as “a,” “an” and “the” is used and using only asingle element is neither explicitly or implicitly defined as beingmandatory, further examples may also use plural elements to implementthe same functionality. Likewise, when a functionality is subsequentlydescribed as being implemented using multiple elements, further examplesmay implement the same functionality using a single element orprocessing entity. It will be further understood that the terms“comprises,” “comprising,” “includes” and/or “including,” when used,specify the presence of the stated features, integers, steps,operations, processes, acts, elements and/or components, but do notpreclude the presence or addition of one or more other features,integers, steps, operations, processes, acts, elements, componentsand/or any group thereof.

Unless otherwise defined, all terms (including technical and scientificterms) are used herein in their ordinary meaning of the art to which theexamples belong.

Embodiments of the present disclosure relate to a use of so-calledmobility modes with distinct grid and pulse matching for differentdoubly dispersive communication links. In other words, embodiments mayrelate to mobility modes for multicarrier filter banks, and may providea grid matching approach. To account for remaining self-interferencewithout the need of estimating channel cross talk coefficients whenselecting a particular mobility mode, in at least some embodiments, theminimum mean square error (MMSE) one-tap equalizer may be tuned toaccount for the self-interference power as well. The approach has beenevaluated for a radio channel generated by the geometry-based statisticQuadriga channel model and with an OTFS transceiver architecture basedon a polyphase implementation for orthogonalized Gaussian andrectangular pulses. Results indicate that, with the appropriate mobilitymode, the potential OTFS gains can be indeed obtained with such tunedequalizers.

Different doubly-dispersive communication channels provide distinctdelay-Doppler spread and diversity characteristics. Particularsingle-dispersive cases therein are time- or frequency-invariantchannels, which yield to simple frequency or time division communicationschemes, respectively. However, for several high mobility environments,the channel becomes dispersive in both time and frequency domain.Especially, vehicular channels may differ in their dissipation in bothdomains time and frequency. Depending on the communication link adistinct spreading region is spanned:

$U:={\left\lbrack {0,\frac{\tau}{B}} \right\rbrack \times \left\lbrack {{- \frac{vB}{L}},\frac{vB}{L}} \right\rbrack}$

where B, L, v, and τ are the bandwidth, length of the filter, Doppler,and delay spread, respectively. In order to cope with doubly-dispersivechannels the synthesis pulse used at the transmitter, the analysis pulseused at the receiver, and their time-frequency grid may match U. Acommon way is therefore to revise the grid, time and frequency spreadsσ_(t) and σ_(f), respectively, of the Gabor pulses with respect to thechannel scattering function of the doubly-dispersive channel

$\begin{matrix}{\frac{T}{F} = {\frac{\sigma_{t}}{\sigma_{f}} =^{!}\frac{\tau_{\max}}{2\upsilon_{\max}}}} & (1)\end{matrix}$

where

$\frac{\tau_{\max}}{2\upsilon_{\max}}$

is the ratio between the maxima of the delay and the Doppler dispersionof the channel. This approach is referred as pulse and grid matching. Inorder to approach the condition (1) of perfect pulse and grid matching,the present disclosure proposes and investigates distinct mobilitymodes.

There are further aspects in pulse design, depending on the scenario. Insome approaches, bi-orthogonality, sometimes called as biorthogonalfrequency division multiplexing (BFDM), may be enforced, which mayenable interference-free communication in additive white Gaussian noise(AWGN) channels. Choosing then, as in some embodiments of the presentdisclosure, synthesis and analysis pulses to be equal in order tomaximize the signal to noise ratio (SNR) for an AWGN channel, yields anorthogonal signaling having even uncorrelated noise contributions.

The present disclosure may provide investigation of OTFS from theclassical angle of pulse-shaped Gabor signaling with additional TFspreading, implemented using Z. Prus̆a et al.: “The Large Time-FrequencyAnalysis Toolbox 2.0,”. The present disclosure may further provide aconsideration of doubly-dispersive vehicular channels in a concretegeometry-based scenario generated by the Quadriga channel (S. Jaeckel etal.: “Quadriga: A 3-d multi-cell channel model with time evolution forenabling virtual field trials)” using pilot-based channel estimation asin U.S. Pat. No. 9,444,514.

Embodiments may provide mobility modes with distinct pulse and gridmatching. Furthermore, at least some embodiments may account for theimpact of the remaining self-interference in the equalizer due toimperfect 2D-deconvolution of the twisted convolution affected by gridand pulse mismatch.

In the following, the OTFS Gabor system model and the OTFS transceiverstructure is introduced. As already mentioned above, OTFS is combinationof pulse shaped multicarrier transmission (with Weyl-Heisenberg/Gaborstructure, i.e., time-frequency translations on a regular grid in thetime-frequency plane) and additional TF spreading using the SFFT.

In the following, the time-frequency grid and pulse shaping, as used inat least some embodiments, is introduced. The frequency resolution maybe defined as

${F = \frac{B}{M}},$

where B is the overall bandwidth and M the number of sub-carriers. Thetime resolution may be defined as

${T = \frac{D}{N}},$

with D the frame duration and N the number of symbols. The timefrequency grid may be sampled with T and F period in the time andfrequency axis, respectively, and may be generated by Λ=diag(T,F) asfollows:

G={(mF,nT),n,m∈Z}  (2)

The entire duration of the transmit Gabor signal may be N·T seconds witha used bandwidth of M·F Hertz. Note that the total duration may dependalso on the dimensioning of the used synthesis and analysis pulse andthe so called time frequency product TF. Gabor (polyphase) filter banksat the transmitter and at the receiver may be configured with pulses γfor the synthesis and g for the analysis of the signals, respectively.The dimensioning of these pulses with respect to the TF grid may betermed as time-frequency localization. For the TF product, three casesmay be distinguished, where the product, TF>1, TF=1, and TF<1—sometimesdenoted as undersampling, critical sampling, and oversampling of thetime-frequency plane, respectively. In at least some aspects of thepresent disclosure, the TF product was chosen as TF=1.25. To enableperfect reconstruction in the nondispersive and noiseless case, thepulses γ and g may be biorthogonal, meaning that:

γ,g(t−nT)e ^(j2πmFt)

=δ(m)δ(n)  (3)

where δ(0)=1 and zero else. Here,

u, v

=∫ū(t)v(t)dt may be used as inner product on L₂(

), the Hilbert space of signals with finite energy. To achieve alsouncorrelated noise contributions, the synthesis and analysis pulse maybe chosen to be equal, resulting in an orthogonal pulse (orthogonal toits time-frequency translates on the time-frequency translates). Given apreliminary prototype pulse, the well-known S^(−1/2) trick may be usedto perform the orthogonalization (constructing a tight Gabor frame onthe adjoint lattice, see e.g. P. Jung and G. Wunder, “WSSUS pulse designproblem in multicarrier transmission”). However, exact orthogonality atthe output of doubly-dispersive channels may be destroyed, resulting inself-interference. By choosing different pulses for the transmitter andreceiver, it may be possible to further reduce the expected power ofself-interference for classes of doubly-dispersive channels (e.g.characterized by the scattering function in a wide-sense stationaryscattering (WSSUS) model).

OTFS may be based on TF-Spreading and De-Spreading. So far, thetransceiver structure is essentially the same as any pulse shapedmulticarrier scheme, like pulse-shaped OFDM, BFDM or filter bankmulticarrier (FBMC). A distinct feature of OTFS is the spreading. Allsymbols X={X_(lk)}_(l,k∈I) where I⊆[M]×[N] may be pre-coded with the socalled SFFT (sometimes also denoted Zak transform) which is furtherdenoted by the linear operator F_(s). The symplectic Fourier transformcontrast from the ordinary 2D Fourier transformation by its signswitching in the exponent and coordinate swapping. This may beinterpreted by mapping an array on discrete delay-Doppler positions (l,k) to an array on grid points (m, n) in the time-frequency plane, sincetime shifts leads to oscillation in frequency and frequency shift causethem in time. More precisely, at the transmitter the pre-coding may bedone by x=F_(s) ⁻¹X with x={x_(mn)}_(m,n∈I) which is:

$\begin{matrix}{x_{mn} = {\sum\limits_{{({l,k})} \in I}{X_{lk}e^{j2{\pi {({\frac{nk}{N} - \frac{ml}{M}})}}}}}} & (4)\end{matrix}$

where x_(mn) is the value transmitted by the transmitter at grid point(m, n) of the time-frequency grid, and X_(lk) is the value at grid point(l, k) of the delay-doppler grid, where I is the set of grid points onthe time-frequency grid and on the delay-doppler grid (which may havethe same dimensions). Since channel estimation and equalization isdiscussed in more detail below, it is only briefly mentioned here thatafter equalization the symbols ŷ={ŷ_(mn)}_(m,n∈I) in the time-frequencyplane are de-spreaded again as Ŷ=F_(s)ŷ with the SFFT:

$\begin{matrix}{{\hat{Y}}_{lk} = {\sum\limits_{{({m,n})} \in I}{{\hat{y}}_{mn}e^{{- j}2{\pi {({\frac{nk}{N} - \frac{ml}{M}})}}}}}} & (5)\end{matrix}$

where ŷ_(mn) is the value received at grid point (m, n) of thetime-frequency grid, and Ŷ_(lk) is the value at grid point (l, k) of thedelay-doppler grid after the SFFT (after de-spreading).

In the following, an exemplary structure of OTFS frames is shown. Insome embodiments, a pilot based channel estimation is used, where apilot is inserted in the delay-Doppler (DD) domain as used in U.S. Pat.No. 9,444,514. The pilot may be sent by the transmitter simultaneouslywith data in the same frame, and due to its design, the channel can beeasily detected at the receiver in the DD domain. FIG. 1 shows anexemplary OTFS frame with pilot 110, guard 120, and data symbols 130 inthe DD domain. The symbols inside the dashed frames 140 may be used forthe channel estimation at the receiver. In detail, the symbols to beplaced in the DD domain may be three fold, i.e. data symbols 130(usually coming from a particular modulation alphabet) are placed onpositions indexed by the set D⊂I (D being the set of data symbols),positions used for channel estimation are defined by the set P⊂I (Pbeing the set comprising pilot 110 and guard symbols 120) with D∩P=Ø(symbols are either used as data symbols or a pilot/guard symbols),which may contain a single pilot symbol and the other positions areunused (can be seen as guard symbols). Hence, it may be set:

P={(l,k):l∈[2W],k∈[4Q]}⊂I  (6)

and an arbitrary location [l=τ, k=2ν] may be used for the non-zero pilotsymbol. Note that W and Q may be defined with respect to the expecteddelay and Doppler shift, respectively. In the following, Q and W werechosen without pretending to reduce the number of guard symbols to anappropriate dimension for each OTFS mode but a constant product of Q·W,i.e. 448 symbols. However, other configurations are feasible.

The non-zero pilot X_(lk)=√{square root over (P_(p))}, may be set at k=1and l=1 (as shown in FIG. 1) with the normalized power of P_(p)=2Q4 Wand all the other symbols may be P are zero-valued guard symbols suchthat

$x_{mn}^{P} = {{\sum\limits_{{({l,k})} \in P}{X_{lk}e^{j2{\pi {({\frac{nk}{N} - \frac{ml}{M}})}}}}} = {\sqrt{P_{p}}e^{j2{\pi {({\frac{n}{N} - \frac{m}{M}})}}}}}$

Thus, summarizing, the OTFS frame in the TF domain may be given by thesuperposition of the pilot and data symbols:

$\begin{matrix}{x_{mn} = {{{\sum\limits_{{({l,k})} \in D}{X_{lk}e^{j2{\pi {({\frac{nk}{N} - \frac{ml}{M}})}}}}} + {\sum\limits_{{({l,k})} \in P}{X_{lk}e^{j2{\pi {({\frac{nk}{N} - \frac{ml}{M}})}}}}}} = {{x_{mn}^{D} + x_{mn}^{P}} = {x_{mn}^{D} + {\sqrt{P_{p}}e^{j2{\pi {({\frac{n}{N} - \frac{m}{M}})}}}}}}}} & (8)\end{matrix}$

The OTFS frame in the time-frequency plane may then be used tosynthesize a transmit signal s(t). This may, for example, be implementedwith a Gabor synthesis filter bank configured with a transmit pulse γ.This can be formally written as:

$\begin{matrix}{{s(t)} = {\sum\limits_{{({m,n})} \in I}{{\gamma \left( {t - {nT}} \right)}e^{{j2\pi}\; {mtFt}}x_{mn}}}} & (9)\end{matrix}$

For a doubly-dispersive channel the noiseless time-continuous channeloutput may consist of (or be based on) an unknown linear combination oftime-frequency translates of the input signal s(t). One way of writingthis formally is to express this operation in terms of a time-varyingconvolution:

$\begin{matrix}{{r(t)} = {{\sum_{p = 1}^{p_{\max}}{{h_{p}(t)}{s\left( {t - \tau_{p}} \right)}}} = {\sum\limits_{{({m,n})} \in I}{x_{mn}{\sum_{p = 1}^{p_{\max}}{{h_{p}(t)}{\gamma \left( {t - \tau_{p} - {nT}} \right)}e^{{j2\pi}\; m\; {F \cdot {({t - \tau_{p}})}}}}}}}}} & (10)\end{matrix}$

where r(t) is the received signal, and where the pth discretepropagation path has delay τ_(p) for p=1 . . . p_(max). The index set Amay be defined as A:=[1 . . . d_(max)]×[1 . . . p_(max)]. Thetime-varying behaviour of h_(p)(t) (the propagation-path andtime-dependent channel) may be given by:

h _(p)(t)=Σ_(d=1) ^(d) ^(max) S _(dp) e ^(j2π·t·v) ^(d)   (11)

where {S_(dp)}_((d,p)∈A) can be understood as the discrete delay-Doppler(DD) spreading function (see for example P. Bello, “Characterization ofrandomly time-variant linear channels”). In particular, this simplifiedmodel implies that each path has the same range of frequency shifts{v_(d)}_(d=1) ^(d) ^(max) but with possibly different coefficients. Inmany cases, it may be assumed that the set of time-frequency shifts{(ν_(d),τ_(p))}_((d,p)∈A) are usually in a box U:=[−ν_(max),ν_(max)]×[0, τ_(max)] of size |U|=2v_(max)τ_(max)<<1, which is alsoknown as the underspread assumption. Putting things together yieldstherefore:

$\begin{matrix}{{r(t)} = {\sum\limits_{{({m,n})} \in I}{x_{mn}{\sum\limits_{{({d,p})} \in A}{S_{dp}{\gamma \left( {t - \tau_{p} - {nT}} \right)} \times {e^{{j2\pi mF} \cdot {({t - \tau_{p}})}} \cdot e^{{j2\pi} \cdot t \cdot \upsilon_{d}}}}}}}} & (12)\end{matrix}$

The received signal may be down-converted and passed into analysisfilter bank (e.g. a Gabor analysis filter bank). The output of the Gaboranalysis filter bank (for exposition, the noiseless case is discussedhere) time-frequency slot (m, n)∈I is then:

$\begin{matrix}{y_{\overset{\_}{m}\overset{\_}{n}} = {{\langle{{{g\left( {t - {\overset{\_}{n}T}} \right)} \cdot e^{j2\pi \overset{¯}{m}Ft}},{r(t)}}\rangle} = {\sum\limits_{{({m,n})} \in I}{x_{mn}{\sum\limits_{({{({d,p})} \in A}}{S_{dp}e^{{- j}2{\pi \cdot m}\; {F \cdot \tau_{p}}} \times {\langle{{{g\left( {t - {\overset{¯}{n}T}} \right)}\ e^{{j2\pi}\overset{\_}{m}{Ft}}},\ {{\gamma \left( {t - \tau_{p} - {nT}} \right)}e^{j2{\pi {({{m\; F} + \upsilon_{d}})}}t}}}\rangle}}}}}}} & \left( {13} \right)\end{matrix}$

where y _(m n) is the value received at grid point (m, n) of thetime-frequency grid (before equalization).

At least some embodiments may be based on the framework and equationslaid out above. In particular, at least some embodiments may relate toOTFS-based communication between a wireless communication device and afurther wireless communication device. This communication may be basedon one of a plurality of communication modes (also denoted “mobilitymodes”), that define the dimension of the grids in the time-frequencyplane and in the delay-Doppler plane.

FIG. 2a shows a block diagram of an embodiment of an apparatus 20 for awireless communication device 200. FIG. 2a further shows the wirelesscommunication device 200 comprising the apparatus 20. FIG. 2b shows ablock diagram of an embodiment of a system comprising the wirelesscommunication device 200 (comprising the apparatus 20) and a furtherwireless communication device 200 a (comprising a correspondingapparatus 20). The wireless communication device and the furtherwireless communication device may be configured to communicate with eachother (e.g. via the corresponding apparatuses 20).

The apparatus 20 comprises a transceiver module 22 for transmitting andreceiving wireless transmissions. The apparatus 20 comprises aprocessing module 24 that is coupled to the transceiver module 22. Forexample, the processing module 24 is configured to control thetransceiver module 22. In general, the processing module 24 may beconfigured to generate data frames to be transmitted via the transceivermodule, and to process data frames that are received via the transceivermodule. These data frames may be used for a communication between thewireless communication device 200 and the further wireless communicationdevice 200 a. Accordingly, the processing module may be configured tocommunicate with a further wireless communication device via thetransceiver module 22. The communication with the further wirelesscommunication device is based on a transmission of data frames betweenthe wireless communication device 200 and the further wirelesscommunication device 200 a. Each data frame is based on atwo-dimensional grid in a time-frequency plane having a time dimensionresolution and a frequency dimension resolution. The processing moduleis configured to perform equalization on received data frames. Theequalization is performed using a minimum mean square equalizer. Theminimum mean square equalizer comprises a term to compensate forself-interference. The processing module 24 may be configured to selecta communication mode from a plurality of communication modes for thecommunication between the wireless communication device and the wirelesscommunication device. The communication mode defines a combination of afrequency dimension resolution and a time dimension resolution of thetwo-dimensional grid in the time-frequency plane.

FIGS. 2c and 2d show flow charts of embodiments of a correspondingmethod for the wireless communication device 200. Features described inconnection with the apparatus and wireless communication devices ofFIGS. 2a to 2b may be likewise applied to the method of FIGS. 2c and/or2 d, e.g. as method steps of the method. The method comprisescommunicating 210 with the further wireless communication device. Themethod may comprise selecting 220 the communication mode from theplurality of communication modes for the communication between thewireless communication device and the wireless communication device. Themethod comprises performing 260 equalization on received data frames.The equalization is performed using a minimum mean square equalizer, theminimum mean square equalizer comprising a term to compensate forself-interference.

The following description relates both to the apparatus and wirelesscommunication devices of FIGS. 2a and/or 2 b, and to the method of FIGS.2c and/or 2 d.

Embodiments of the present disclosure relate to wireless communicationdevices and to an apparatus, a method and a computer program of suchwireless communication devices. In the following, two wirelesscommunication devices may be assumed that communicate with each other.This communication is usually performed using wireless transmissionsthat are exchanged between the two wireless communication devices over a(wireless) channel. In at least some embodiments, the channel may beassumed to be a doubly-dispersive channel. This communication may besub-divided into smaller and smaller units. In general, in wirelesscommunication, a frame or data frame is considered to be a coherent unitthat comprises or represents a plurality of symbols. For example, aframe may be defined as cyclically repeated data block that comprises(or consists of) one or a plurality of time slots. In these time slots,data may be transmitted via a plurality of different carrierfrequencies. For example, in embodiments each frame comprises aplurality of time slots, which are transmitted via a plurality ofcarrier frequency. Correspondingly, the data frame may be considered tobe transmitted in the time frequency plane, wherein the time slots spanacross the time dimension of the time-frequency plane, and wherein thecarrier frequencies span across the frequency dimension of thetime-frequency plane. This time-frequency plane can be used to model a(logical) grid that spans via the time dimension and the frequencydimension. This is a logical construct, which is, during transmission ofthe data frames, mapped to the time slots and carrier frequencies. Ingeneral, this grid in the time-frequency plane is delimited by thebandwidth range being used to transmit the data frame, and by the timethat is used to transmit the frame (the time being subdivided into theone or the plurality of time slots). Accordingly, in embodiments, eachdata frame is based on a two-dimensional grid in a time-frequency planehaving a time dimension resolution and a frequency dimension resolution.

In at least some embodiments, the data frames are OrthogonalTime-Frequency Spreading (OTFS) data frames, e.g. having the propertiesthat have been laid out above. For example, each data frame (or a subsetof the data frames) may be based on the frame structure shown in FIG. 1.In this case, the data frame that is transmitted in time and frequencyis derived from a different representation of data, from thedelay-Doppler representation. In the delay-Doppler representation,signals are represented in the delay-Doppler plane. The delay-Dopplerrepresentation can be transformed using the so-called (inverse)Symplectic Finite Fourier Transform (SFFT) to obtain the time-frequencyrepresentation. Accordingly, the two-dimensional time-frequency grid maybe derived from the two-dimensional grid in a delay-Doppler plane havinga delay dimension and a Doppler dimension. For example, thetwo-dimensional time-frequency grid may be derived from thetwo-dimensional grid in a delay-Doppler plane having a delay dimensionand a Doppler dimension using the inverse SFFT. To transform the gridfrom the time-frequency plane to the delay-Doppler plane, the SFFT maybe used. During signal processing, e.g. by the processing module, thegrids in the delay-Doppler plane and the time-Frequency plane may berepresented using two-dimensional matrices, wherein each element of thematrix represents an element of the corresponding grid. Thecorresponding operations, e.g. the SFFT and the inverse SFFT, may beperformed on the matrix representing the respective grid.

In general, the processing module may be configured to receive and/ortransmit the data frames via the transceiver module 22. Accordingly, themethod may comprise transmitting and/or receiving data frame, e.g. via atransceiver module of the wireless communication device, such as thetransceiver module 22. Accordingly, the processing module may beconfigured to generate the data frames that are to be transmitted. Forexample, the processing module 24 may be configured to generate a dataframe for the communication from a plurality of data symbols bygenerating, for each data symbol, a localized pulse. Accordingly, themethod may comprise generating 270 the data frame for the communicationfrom the plurality of data symbols by generating 272, for each datasymbol, a localized pulse. This localized pulse may represent the datasymbol. For example, a Quadrature Amplitude Modulation may be used torepresent the data symbol within a localized pulse. In variousembodiments, the localized pulse may be generated using a quasi-periodicfunction, i.e. a function that is periodic up to a multiplicative phase.The processing module may be further configured, in order to generatethe data frame, to place the localized pulse on a point on thetwo-dimensional grid in the delay-Doppler plane. In other words, inorder to generate the data frame, the method may comprise placing 274the localized pulse on a point on the two-dimensional grid in thedelay-Doppler plane. Again, this is merely an illustrativerepresentation. Within the processing module, each point of the grid maybe represented by an element of the matrix for the delay-Dopplerrepresentation. The processing module may be further configured, inorder to generate the data frame, to transform the plurality oflocalized pulses on the delay-Doppler plane onto the time-frequencyplane using an inverse symplectic Fourier transform. In other words, inorder to generate the data frame, the method may comprise transforming276 the plurality of localized pulses on the delay-Doppler plane ontothe time-frequency plane using the inverse symplectic Fourier transform.Again, this operation may be performed on the elements of the matrixrepresenting the grid in the delay-Doppler plane, to obtain the matrixthat represents the grid in the time-frequency plane. The processingmodule may be further configured to transmit the generated data framevia the transceiver module 22 (to the further wireless communicationdevice). In other words, the method may comprise transmitting 278 thegenerated data frame (via a transceiver module of the wirelesscommunication device). This may be done using a sequence ofmulti-carrier symbols.

Correspondingly, the processing module may be configured to process thereceived data frames. For example, the processing module 24 may beconfigured to receive a data frame via the transceiver module 22.Accordingly, the method may comprise receiving 240 the data frame. Theprocessing module may be configured to transform the data frame from thetime-frequency plane into the delay-Doppler plane (e.g. using an SFFT onthe matrix representing the grid in the time-frequency plane). Themethod may comprise transforming 248 the data frame from thetime-frequency plane into the delay-Doppler plane. The processing modulemay be configured to demodulate a plurality of localized pulses at thepoints of the two-dimension plane in the delay-Doppler plane.Accordingly, the method may comprise demodulating 249 the plurality oflocalized pulses at the points of the two-dimension plane in thedelay-Doppler plane. The plurality of localized pulses may represent aplurality of data symbols that were transmitted using the received dataframe.

In general, both the wireless communication device and the furtherwireless communication device may be any type of wireless communicationdevice, e.g. mobile communication devices, such as smartphones,wearables, mobile sensors or wireless communication devices of vehicles,or stationary wireless communication devices, such as base stations orroadside stations (if used in a vehicular context. Accordingly, thewireless communication device and/or the wireless communication devicemay be one of a mobile wireless communication device, a vehicularwireless communication device, a stationary wireless communicationdevice and a base station. For example, the wireless communicationdevice may be a vehicular wireless communication device (e.g. of avehicle that drives along a road), and the further wirelesscommunication device may be a stationary wireless communication device,such as a roadside unit that is placed at the side of the road or a basestation of a (vehicular) mobile communication system. Accordingly, thecommunication between the wireless communication device and the furtherwireless communication device may be a communication via a vehicularcommunication protocol. In more general terms, however, embodiments maybe used with any kind of mobile communication system that supportsframes comprising a plurality of time slots and a plurality ofsubcarriers. Accordingly, the wireless communication device and thefurther wireless communication device may communicate via a mobilecommunication system may, for example, one of the Third GenerationPartnership Project (3GPP)-standardized mobile communication networks.The mobile or wireless communication system may correspond to, forexample, a 5th Generation system (5G), a Long-Term Evolution (LTE), oran LTE-Advanced (LTE-A)-based mobile communication system. In otherwords, the data frames may be data frames of a mobile communicationsystem.

As laid out above, grids (in the time-frequency plane and in thedelay-Doppler plane) are used to represent the signals. In OTFS,computationally feasible equalizers may suffer from mismatchedtime-frequency grids. Parity may be achieved with perfect gird matchingof the Gabor synthesis and analysis pulses with the delay and Dopplerspread of the channel. However, this might not be achieved in practicedue to the varying mobility of users, and correspondingly changingchannels. This may lead to performance degradation (higher error rates).In OTFS, different channel conditions and appropriate grid matching havenot been studied. When such an OTFS system is implemented, performancedegradation may be observed, and the expected performance might notachieved. In many cases, this may be caused by a mismatch of the grid,as perfect grid matching is assumed in publications related to OTFS sofar. Unfortunately, grid mismatch may cause significant performancedegradations for an OTFS system, as is later shown in FIGS. 3a to 4d .Embodiments may thus use mobility modes (i.e. communication modes) withdistinct grid-matching for different doubly dispersive communicationlinks (i.e. channels). For example, a communication mode may provide ahigh Doppler and less delay resolution or high delay and less Dopplerresolution or an equal resolution in both domains and furtherconstellations.

In embodiments, the processing module 24 is configured to select acommunication mode from a plurality of communication modes for thecommunication between the wireless communication device and the wirelesscommunication device. In general, the selection of the communicationmode may be seen akin to choosing a time resolution and frequencyresolution for the grid in the time-frequency plane that matches thechannel that is used for the communication between the wirelesscommunication devices. For example, in different scenarios, signalstransmitted via the channel may experience different amounts of delayspread and Doppler spread. To account for such different channels, thegrid may be chosen such that the respective properties of the channelare taken into account. For lower relative velocities, less resolutionin the time domain may be required, and a higher resolution in thefrequency domain may be desired if higher delays occur. For example, athigher relative velocities, a grid having a higher resolution (i.e. morepoints) in the time dimension may be advantageous (to allow for a higherDoppler spread), while at lower relative velocities, a grid having ahigher resolution (i.e. more points) in the frequency dimension may beadvantageous.

In general, it may be possible to select “the” perfect grid for eachcommunication. In practice however, it may be more useful to limit thenumber of grid configurations (or communication modes), in order toreduce an implementation complexity of the wireless communicationdevice. Accordingly, the plurality of communication modes may be apre-defined set of communication modes (i.e. having a fixed number ofcommunication modes). For example, the plurality of communication modesmay be pre-defined by a mobile communication system being used for thecommunication. For example, the plurality or pre-defined set ofcommunication modes may comprise at least three, or at least five, atleast seven different communication nodes. For example, the plurality ofpre-defined set of communication modes may comprise at most 16, or atmost 8, at most 5, or at most three communication modes. For example,the communication modes of the plurality of communication modes may beidentified using an identifier, which may be transmitted between thewireless communication devices to negotiate the communication mode thatis to be selected for the communication.

The communication mode defines a combination of a frequency dimensionresolution and a time dimension resolution of the two-dimensional gridin the time-frequency plane. In other words, the communication mode maydefine a number of points N along a time dimension of thetwo-dimensional grid in the time-frequency plane and a number of pointsM along a frequency dimension of the two-dimensional grid in thetime-frequency plane. Accordingly, the time dimension resolution maydefine a number of points N along a time dimension of thetwo-dimensional grid in the time-frequency plane. The frequencydimension resolution may define a number of points M along a frequencydimension of the two-dimensional grid in the time-frequency plane. Thesemay be the same dimensions that are used for the grid in thedelay-Doppler plane. For example, M may be the number of points alongthe delay dimension of the two-dimensional grid in the delay-Dopplerplane, and N may be the number of points along the Doppler dimension ofthe two-dimensional grid in the delay-Doppler plane. For example, thetwo-dimensional grid in the time-frequency plane and/or thetwo-dimensional grid in the time-frequency plane may have M×N points.

In some embodiments, there may be constraints that limit the number ofdifferent communication modes. For example, both N and M may be a powerof two. Additionally, the product of N and M may be the same for all ofthe communication modes. In other words, the product of the number ofpoints along the time dimension and the number of points along thefrequency dimension of the two-dimensional grid in the time-frequencyplane may be the same for the communication modes of the plurality ofcommunication modes.

In at least some embodiments, the plurality (or pre-defined set) ofcommunication modes may comprise at least one communication mode that issuitable for a broad range of communication nodes. Such communicationmodes may, for example, be used as a default communication mode, thatmay be initially used when the communication between the wirelesscommunication devices is established. In general, such communicationmodes may be found for values of N and M that are within the same orderof magnitude. For example, the plurality of communication modes maycomprise at least one communication mode defining a combination of afrequency dimension resolution and a time dimension resolution whereinM≤N and 4M≥N or wherein M≥N and M≤4N. In particular, the plurality ofcommunication modes may comprise at least one communication modedefining a combination of a frequency dimension resolution and a timedimension resolution wherein M=N (i.e. the same number of points alongthe time and the frequency dimension). Such a communication modes may beused as default communication mode.

Other communication modes may either satisfy M>N or M<N. For example,the plurality of communication modes may comprise at least onecommunication mode defining a combination of a frequency dimensionresolution and a time dimension resolution wherein M>N. For example, theplurality of communication modes may comprise at least one communicationmode defining a combination of a frequency dimension resolution and atime dimension resolution wherein M≥4N, at least one communication modedefining a combination of a frequency dimension resolution and a timedimension resolution wherein M≥16N, and/or at least one communicationmode defining a combination of a frequency dimension resolution and atime dimension resolution wherein M≥256N. Such communication modes maybe used in scenarios with low relative velocities.

Additionally or alternatively, the plurality of communication modes maycomprise at least one communication mode defining a combination of afrequency dimension resolution and a time dimension resolution whereinM<N. For example, the plurality of communication modes may comprise atleast one communication mode defining a combination of a frequencydimension resolution and a time dimension resolution wherein 4M≤N, atleast one communication mode defining a combination of a frequencydimension resolution and a time dimension resolution wherein 16M≤N,and/or at least one communication mode defining a combination of afrequency dimension resolution and a time dimension resolution wherein256M≤N. Such communication modes may be used in scenarios with higherrelative velocities.

In addition to the dimensions of the grid, the communication mode mayalso define the pulse shape to be used (e.g. when modulating theplurality of symbols in the delay-Doppler plane). In other words, thecommunication mode may define a pulse shape to use for thecommunication. For example, the pulse shape may be one of a Gaussianpulse, a rectangular pulse, and another pulse form.

In general, communication modes may be selected at least two timesduring the communication—initially, i.e. for the first wirelesstransmission (of a communication session) between the wirelesscommunication device and the further wireless communication device, andduring the communication (session), e.g. in order to select acommunication mode that better fits the channel between the wirelesscommunication devices. When using different time-frequency gridsdepending on the radio channel conditions some grids match the channelgood others not so much. In fact, if the wrong grid is selected theperformance and hence the bit error rate (BER) might increasedrastically. This might not be acceptable in some cases as for e.g. forthe control channel and some negotiation phases between transmitter andreceiver.

Therefore, the processing module may be configured to initially select acommunication mode for the communication, i.e. to select a communicationto use for a first data frame being exchanged between the wirelesscommunication devices. In other words, the processing module 24 may beconfigured to initially select a default communication mode of theplurality of the plurality of communication modes for the communicationbetween the wireless communication device and the further wirelesscommunication device. Accordingly, the method may comprise initiallyselecting 222 a default communication mode of the plurality of theplurality of communication modes for the communication between thewireless communication device and the further wireless communicationdevice.

In various embodiments, a default communication mode (or “safe”communication mode) may be initially selected. For example, the safemode may be a grid scaling mode (time-frequency grid) having an averageperformance, which may be used in almost all environments. Such a safemode may be chosen with an equal time-frequency resolution. In general,the plurality or pre-defined set of communication mode may comprise asingle (or low number, such as three) default communication mode. Thiscommunication mode may be a communication mode that works in a varietyof scenarios. For example, the default communication mode may be a“robust” communication mode, in the sense, that it does not requirespecific channel properties in order to provide adequate performance. Inother words, the default communication mode may be a communication modethat provides robust grid matching in a plurality of differentdelay-spread and Doppler-spread scenarios.

Such a default communication mode may, for example, have values of M andN that are in the same order of magnitude. For example, the defaultcommunication mode may defines a combination of a frequency dimensionresolution and a time dimension resolution wherein M≤N and 4M≥N orwherein M≥N and M≤4N, e.g. where M=N. M and N may also be chosen such,that there are other communication modes that have lower and highervalues of M and N. In other words, the default communication mode maydefine a combination of a frequency dimension resolution and a timedimension resolution wherein the number of points N along the timedimension is larger than a minimal number of points N_(min) and smallerthan a maximal number of points N_(max) along the time dimension, andwherein the number of points M along the frequency dimension is largerthan a minimal number of points M_(min) and smaller than a maximalnumber of points M_(max) along the frequency dimension. The minimalnumber of points and the maximal number of points along the time orfrequency dimension may be defined by other communication modes of theplurality of communication modes, i.e. N_(max) may be the highest valueof N among the plurality of communication modes, and N_(min) may be thelowest number of N among the plurality of communication modes.Accordingly, M_(max) may be the highest value of M among the pluralityof communication modes, and M_(min) may be the lowest number of M amongthe plurality of communication modes.

Alternatively, a trial-and-error strategy may be employed. How does thereceiver know which grid scaling was used by the transmitter if gridscaling is not static and changes depending on the radio conditions? Thereceiver may (need to) use the same grid at the matched filter as thetransmitter has used. In other systems, a static grid may be used. Inembodiments, however, a plurality of communication modes may be used.For example, the plurality of communication may comprise (at least)three different grids. The first grid with high Doppler and low delayresolution, the second with low Doppler and high Delay resolution, andthe third with equal delay Doppler resolution. The transmitter may (needto) use one of these grids (e.g. of the three grids) which are used atthe receiver. In embodiments, the receiver may use several grids for thematched filter and select the grid which leads to the lowest BER.

For example, when receiving a (first) data frame from the wirelesscommunication device, the processing module may process the receiveddata frame using matched filters that are based on two or morecommunication modes (e.g. three communication modes, dependent on thenumber of filter banks that can be used in parallel), in order to findout which communication mode was selected. In other words, theprocessing module 24 may be configured to receive a data frame from thefurther wireless communication device via the transceiver module 22.Accordingly, the method may comprise receiving 240 a data frame from thefurther wireless communication device. The processing module 24 may beconfigured to process the received data frame using matched filters thatare based on two or more communication modes of the plurality ofcommunication modes. The corresponding method may comprise processing242 the received data frame using matched filters that are based on twoor more communication modes of the plurality of communication modes. Theprocessing may be performed in parallel, e.g. in order to quicklyevaluate two, three or more communication modes at the same time. Inother words, the processing module 24 may be configured to process thereceived data frame in parallel using the matched filters that are basedon the two or more communication modes. Accordingly, the received dataframe may be processed 242 in parallel using the matched filters thatare based on the two or more communication modes. For this, a pluralityof filter banks may be used that are based on the matched filters thatare based on the two or more communication modes. In other words, theprocessing module 24 may be configured to use a plurality of filterbanks that are based on two or more communication modes of the pluralityof communication modes to process the received data frame. The methodmay comprise using 246 a plurality of filter banks that are based on twoor more communication modes of the plurality of communication modes toprocess 242 the received data frame. Alternatively or additionally, amulti-step procedure may be used wherein matched filters that are basedon a first (or two or more first) communication mode(s) are used in afirst time-step, and wherein matched filters that are based on a second(or two or more second) communication mode(s) are used in a firsttime-step, the first and second communication mode(s) being different.In this case, subsequently, a number of different communication modesmay be tried until the correct communication mode is selected.

The selection of the communication mode may be based on a result of theprocessing. For example, a result of the processing may be a bit-errorrate that is achieved after the data frame is demodulated based on thematched filters that are based on the two or more differentcommunication modes. If the matched filters of one of the communicationmodes yields a low bit-error rate, the respective communication mode maybe selected. In other words, the processing module 24 may be configuredto determine bit-error rates that result from the use of the matchedfilters that are based on the two or more communication modes. Theprocessing module may be configured to select the communication modebased on the determined bit-error rates (e.g. by selecting thecommunication mode yielding the lowest bit-error rate). Accordingly, themethod may comprise determining 244 bit-error rates that result from theuse of the matched filters that are based on the two or morecommunication modes. The method may comprise selecting 220 thecommunication mode based on the determined bit-error rates.

After the communication has been initiated, the communication mode to beused for the (future) communication may be changed. In other words, thecommunication between the wireless communication device and the furtherwireless communication device may comprise a plurality of data framesthat are transmitted between the wireless communication device and thefurther wireless communication device. The processing module 24 may beconfigured to change the communication mode during the communicationbetween the wireless communication device and the further wirelesscommunication device, e.g. by selecting a different communication modefrom the plurality of communication modes (i.e. different from aninitially or previously selected communication mode). Accordingly, themethod may comprise changing 224 the communication mode during thecommunication between the wireless communication device and the furtherwireless communication device, e.g. by selecting 226 a differentcommunication mode from the plurality of communication modes.

In various embodiments, the communication that is selected for thecommunication, e.g. when initiating the communication, or when thecommunication mode is changed during the communication, may be selectedon one or more selection criteria (also termed “mobility modeselection”). But how does the transmitter find an appropriate gridscale, in order to avoid performance degradation? In conventional OTFSsystems, the grid is constant and defined in the standard. Inembodiments, on the other hand, the processing module may be configuredto estimate the spreading function and hence the characteristics of theradio channel (delay, Doppler). Accordingly, one of the criteria forselecting a communication mode may be a spreading function (i.e. a delayspread and/or a Doppler spread) of the channel that is used for thecommunication. The spreading function, may, in turn be used to selectthe appropriate communication mode.

Accordingly, the processing module 24 may be configured to select thecommunication mode from the plurality of communication modes based on anestimated self-interference of the plurality of communication modes. Ingeneral, self-interference is interference that is caused by the signalitself, e.g. due to delays caused by multipath propagation or due tofrequency shifts that happen due to the Doppler effect. For example, theself-interference incurred at a symbol of a plurality of symbols of thedata frame may originate from the other symbols of the plurality ofsymbols of the data frame. Accordingly, a self-interference of acommunication node may be a self-interference that is incurred whenselecting said communication mode. The self-interference of acommunication mode is based on the channel that is used forcommunicating—different channels may lead to different amounts and/orproperties of self-interference. The self-interference may becharacterized by two terms—the delay spread and the Doppler spread. Inother words, the self-interference may be based on the delay-Spread andthe Doppler spread of the channel, and based on the communication modethat is selected for the communication.

The delay spread and the Doppler spread may also be denoted the“spreading function” of the channel.

Accordingly, the processing module may be configured to estimate theself-interference using a previously received data frame. Accordingly,the method may comprise estimating 230 the self-interference using apreviously received data frame. This can be done based on the receivedpilot tone of the OTFS frame in the delay Doppler domain. For example,each data frame may comprise a (single) pilot symbol, a plurality ofguard symbols, and a plurality of data symbols (see, for example,FIG. 1) (in the delay-Doppler representation/on the two-dimensionaldelay-Doppler grid). The processing module 24 may be configured toestimate the self-interference using the pilot symbol of a previouslyreceived data frame. Accordingly, the method may comprise estimating 230the self-interference using the pilot symbol of a previously receiveddata frame. In particular, the spreading function may be determinedusing the pilot symbol. In other words, the processing module 24 may beconfigured to determine a spreading function of a channel that is usedfor the communication based on the pilot symbol of the previouslyreceived data frame. Accordingly, the method may comprise determining232 the spreading function of a channel that is used for thecommunication based on the pilot symbol of the previously received dataframe. In other words, the self-interference (or spreading function) maybe classified based on received pilot(s) tone in the past.

In various embodiments, the self-interference, and therefore thespreading function, may be determined by merely de-spreading componentsof the received data frame that belong to the guard symbols (and thepilot symbol), and deduce the self-interference from the respectiveterms. In other words, each data frame may comprise a plurality of guardsymbols surrounding the pilot symbol on the two-dimensional grid in thedelay-Doppler plane. The processing module 24 may be configured toperform a symplectic Fourier transform on the received data frame (i.e.the de-spreading). Accordingly, the method may comprise performing 234 asymplectic Fourier transform on the received data frame. The symplecticFourier transform may be performed for the points on the two-dimensionalgrid in the delay-Doppler plane corresponding to the pilot symbol andthe subset of the plurality of guard symbols (see e.g. equations 7 and20). The spreading function may be determined using a result of thesymplectic Fourier transform. In other, the result of the symplecticFourier transform may indicate the self-interference and/or thespreading function of the channel.

The processing module 24 may be configured to select the communicationmode based on the spreading function of the channel. For this, theapproach proposed by Jung and Wunder in “WSSUS pulse design problem inmulticarrier transmission” may be used. Under a fixed-bandwidthconstraint W and a fixed-bandwidth efficiency E (in complex symbols), anoptimal number for N (the number of points on the frequency dimension,i.e. the number of subcarriers) may be calculated. For example, thefollowing may be given:

${{TF} = {{\epsilon^{- 1}\mspace{14mu} {assuming}\mspace{14mu} \Lambda} = {{diag}\mspace{11mu} \left( {T,F} \right)}}},{\frac{T}{F} = \frac{\tau_{d}}{2\upsilon_{d}}},{{{and}\mspace{14mu} F} = \frac{W}{N}}$

(see e.g. equations 1 and 2).

$N = {{W \cdot \sqrt{\frac{\tau_{d}}{2{\epsilon \cdot \upsilon_{d}}}}} = {W \cdot \sqrt{\frac{\tau_{d}c}{2{\epsilon \cdot {vf}_{c}}}}}}$

where τ_(d) is the delay spread, v_(d) is the Doppler spread, v is thespeed between wireless communication device and further wirelesscommunication device (transmitter and receiver), c the speed of light,and f_(c) the carrier frequency. Moreover, in FFT-based polyphasefiltering, N may be power of two. The above formula represents atradeoff between time and frequency-division multiplexing intime-variant channels.

The N that was calculated above may be used to select a communicationmode from the plurality or -predefined set of communication modes (byselecting the communication having an N that is closest to the N thatwas calculated using the formula above). The pre-defined set ofcommunication nodes may represent communication nodes that are allowedfor the communication and/or known by the receiver.

The above equation represents a concrete implementation of adetermination of a value for N. Other implementations are possible. Ingeneral, the processing module 24 may be configured to select thecommunication mode based on a delay spread of a channel that is used forthe communication and based on a relative velocity between the wirelesscommunication device and the further wireless communication device (seee.g. the third part of the equation). The processing module 24 may beconfigured to select the communication mode further based on spectralefficiency, based on a bandwidth, and based on a carrier frequency ofthe communication.

In some embodiments, the communication mode may define a pulse shape touse for the communication. Accordingly, the processing module may beconfigured to select a pulse shape from a plurality of pulse shapes(e.g. a pre-defined set of pulse shapes), and select the communicationmode based on the selected pulse shape. The method may compriseselecting a pulse shape from a plurality of pulse shapes, and selectingthe communication mode based on the selected pulse shape. In general, asuitability of a pulse shape for a certain channel (and combination of Nand M) is based on two parameters—a channel gain that can be obtainedusing a pulse shape at a point of the delay-Doppler (or time-frequency)grid, and a self-interference power incurred using the pulse shape (fromthe other points of the delay-Doppler (or time-frequency) grid). Ingeneral, the better the ratio of channel gain over self-interferencepower, the more suitable the pulse shape is for that channel. This ratiomay also be used to calculate the Signal-to-Interference-and-Noise-Ratio(SINR) for the pulse shape. In some embodiments, the processing modulemay be configured to select the pulse shape based on the ratio ofchannel gain over self-interference power of the pulse shapes of theplurality of pulse shapes. In some embodiments, the processing modulemay be configured to determine a suitable pulse shape by iterativelymaximizing the channel gain of the pulse shape and by iterativelyminimizing the self-interference of the pulse shape. Accordingly, themethod may comprise determining a suitable pulse shape by iterativelymaximizing the channel gain of the pulse shape and by iterativelyminimizing the self-interference of the pulse shape. In general, thepulse shape may be selected from the plurality of pulse shapes based onthe determined, suitable pulse shape. For example, the pulse shape maybe determined using the approach taken in section III of Jung and Wunderin “WSSUS pulse design problem in multicarrier transmission”.

In general, if grid scaling and pulse-shaping are used, then the samegrid (i.e. communication mode) may (need to) be selected at thetransmitter as well as at the receiver. In case that the transmitterselect a different grid as the receiver, then the receiver might not beable to demodulate the wave form. This selection may be performedunilaterally, i.e. the wireless communication device that initiates theconnection selects the communication mode, and the other follows suit.Alternatively, the wireless communication device may be decided uponbilaterally. For example, a negotiation may be performed between thewireless communication devices. In other words, the wirelesscommunication devices may perform mobility mode negotiation. In otherwords, communication/mobility mode (grid scaling/pulse-shaping)negotiation may be done between transmitter and receiver.

For example, in an exemplary embodiment, at a first step, thecommunication node 1 (e.g. either the wireless communication device orthe further wireless communication device) which starts thecommunication begins to use a time-frequency grid that is also known bythe receiving node 2 (the other of the wireless communication device),for example the default communication mode. At a second step, thereceiving node 2 may be able to calculate the best grid scaling/pulseshaping using the spreading function, e.g. based on Jung and Wunder:“WSSUS pulse design problem in multicarrier transmission”. Accordingly,the receiving node may propose a time-frequency grid and pulse shaping(obtained from (1)) to node 1. At a third step, node 1 sends itsacceptance to node 2 or proposes a new grid scaling, and requestsacceptance from node 2. At a fourth step, node 2 and node 1 may changetheir grids and communicate with the new grid scaling (i.e. with a newcommunication mode).

In more general terms, the processing module 24 may be configured tonegotiate a communication mode of the plurality of communication modesto select for future communication between the wireless communicationdevice and the further wireless communication device with the furtherwireless communication device. Accordingly, the method may comprisenegotiating 250 a communication mode of the plurality of communicationmodes to select for future communication between the wirelesscommunication device and the further wireless communication device withthe further wireless communication device.

As stated above, the processing module 24 may be configured to initiallyselect a communication mode that is known at the wireless communicationdevice and at the further wireless communication device for thecommunication between the wireless communication device and the furtherwireless communication device. Accordingly, the method may compriseinitially selecting 222 a communication mode that is known at thewireless communication device and at the further wireless communicationdevice for the communication between the wireless communication deviceand the further wireless communication device. This may either be adefault communication mode, or a communication mode that was used for aprevious communication between the wireless communication devices. Inother words, the processing module 24 may be configured to initiallyselect a default communication mode for the communication between thewireless communication device and the further wireless communicationdevice. Accordingly, the method may comprise initially selecting 222 adefault communication mode of the plurality of the plurality ofcommunication modes for the communication between the wirelesscommunication device and the further wireless communication device.Alternatively, the processing module 24 may be configured to initiallyselect a communication mode that was selected for a previouscommunication between the wireless communication device and the furtherwireless communication device for the communication between the wirelesscommunication device and the further wireless communication device, e.g.for the latest previous communication between the wireless communicationdevice and the further wireless communication device. Accordingly, themethod may comprises initially selecting 222 a communication mode thatwas selected for a previous communication between the wirelesscommunication device and the further wireless communication device forthe communication between the wireless communication device and thefurther wireless communication device.

The initially selected communication mode may be used to negotiate thecommunication to select for a future communication between the wirelesscommunication device and the further wireless communication device. Insome embodiments, the negotiation may be initiated by the wirelesscommunication device. For example, the processing module 24 may beconfigured to transmit information about a communication mode to selectfor a future communication between the wireless communication device andthe further wireless communication device to the further wirelesscommunication device (e.g. by transmitting an indicator to the furtherwireless communication device). Accordingly, the method may comprisetransmitting 252 information about a communication mode to use for afuture communication between the wireless communication device and thefurther wireless communication device to the further wirelesscommunication device. For example, the information about thecommunication mode may be transmitted using the initially selectedcommunication mode. The processing module may be configured to selectthe communication mode for the future communication with the furtherwireless communication device, e.g. if an acknowledgement (or nonegative acknowledgement) is received from the further wirelesscommunication device. Accordingly, the method may comprise selecting 220the communication mode for the future communication with the furtherwireless communication device. Again, the communication mode to beselected may be selected based on the spreading function of the channel.In other words, the processing module 24 may be configured to select thecommunication mode for the future communication based on the spreadingfunction of the channel (e.g. as shown above). Accordingly, the methodmay comprise selecting 220 the communication mode for the futurecommunication based on the spreading function of the channel.

In some cases, the negotiation may be initiated by the further wirelesscommunication device, or the further wireless communication device mayprovide a counterproposal if it disagrees with the transmittedinformation on the communication mode. In this case, information about acommunication mode to select for a future communication between thewireless communication device and the further wireless communicationdevice may be received from the further wireless communication device.In other words, the processing module 24 may be configured to receiveinformation about a communication mode to select for a futurecommunication between the wireless communication device and the furtherwireless communication device from the further wireless communicationdevice. Accordingly, the method may comprise receiving 254 informationabout a communication mode to use for a future communication between thewireless communication device and the further wireless communicationdevice from the further wireless communication device. Similar to thereverse direction indicated above, the information about thecommunication mode may comprise an indicator of the communication codeto select for the future communication, or may otherwise indicate thecommunication mode to use. In general, the communication mode indicatedby the information about the communication mode may be comprised in theplurality of communication modes. Furthermore, the communication modeindicated by the information about the communication mode may be boththe wireless communication device and the further wireless communicationdevice. The processing module 24 may be configured to select thecommunication mode for the future communication with the furtherwireless communication device. Accordingly, the method may compriseselecting 220 the communication mode for the future communication withthe further wireless communication device.

In some cases, the communication mode proposed by the further wirelesscommunication device may be selected “as is” for the futurecommunication. Alternatively, the wireless communication device that hasreceived the information about the communication may examine, whetherthe communication mode is suitable, e.g. based on the properties of thechannel, and/or based on the capabilities of the wireless communicationdevice. In other words, the processing module 24 may be configured toexamine the information about the communication mode to select forfuture communication based on an examination criterion. Accordingly, themethod may comprise examining 256 the information about thecommunication mode to use for future communication based on theexamination criterion. For example, the examination criterion may bebased on the spreading function of the channel used for thecommunication. For example, the wireless communication device may beconfigured to determine an optimal M and/or N based on the spreadingfunction of the channel, and to compare the M and/or N of thecommunication mode of the received information about the communicationmode with the optimal M and/or N (and to deem the examination criterionnot fulfilled if the discrepancy is too large). Additionally oralternatively, the examination criterion may be based on thecapabilities of the wireless communication device. For example, if thewireless communication device does not support the communication mode ofthe received information about the communication mode, the examinationcriterion may be deemed not fulfilled. Based on whether the examinationcriterion is deemed fulfilled, two options present themselves: If theexamination criterion is deemed fulfilled, the wireless communicationdevice may select the communication mode of the received informationabout the communication mode, if not, the wireless communication devicemay ask for another proposal, or may provide an alternativecommunication mode. In other words, the processing module 24 may beconfigured to select the communication mode for the future communicationwith the further wireless communication device if the communication modeto use for future communication if the examination criterion isfulfilled. Accordingly, the method may comprise selecting 220 thecommunication mode for the future communication with the furtherwireless communication device if the communication mode to use forfuture communication if the examination criterion is fulfilled. Theprocessing module 24 may be configured to transmit a response to thefurther wireless communication device if the examination criterion isnot fulfilled. Accordingly, the method may comprise transmitting 258 aresponse to the further wireless communication device if the examinationcriterion is not fulfilled. The response may comprise information aboutan alternative communication mode to use for the future communication.Again, the information about the alternative communication may comprisean indicator of the alternative communication mode.

Similar to above, the processing module may be configured to select thealternative communication mode. For example, the processing module 24may be configured to select the alternative communication mode for thefuture communication based on the spreading function of the channel.Accordingly, the method may comprise selecting 257 the alternativecommunication mode for the future communication based on the spreadingfunction of the channel.

In general, both wireless communication devices may be configured totransmit and receive the information about the (alternative)communication mode to select for the future communication between thewireless communication device and the further wireless communicationdevice, and to use the appropriate functionality, depending on whichwireless communication device initiates the negotiation. The processingmodule 24 may be configured to change the communication mode of thecommunication based on the transmitted and/or receive information aboutthe communication mode, e.g. at a point in time indicated by theinformation about the communication mode. Accordingly, the method maycomprise changing the communication mode of the communication based onthe transmitted and/or receive information about the communication mode.

In the following, the channel estimation, the equalization and aself-interference which remains in the OTFS transceiver structure thatis caused by pulse and grid mismatch is discussed. In particular, thelink between the equalization as a 2D deconvolution and the true channelmapping, given as a twisted convolution, is shown. In particular, thedifference between twisted convolution and regular 2D-deconvolution mayamount to self-interference.

In embodiments, the impact of self-interference may be quantified. Inorder to reveal the impact of pulse and grid mismatch in terms ofself-interference, the inner product in (13) may be rewritten andcomputed separately. In the context of this application, ⋅ may denotethe down-converted and passed into the filterbank values and ⋅* maydenote the conjugate transpose). Substituting t=t−nT gives

${\langle{{{g\left( {t - {\overset{¯}{n}T}} \right)}e^{j2\pi \overset{¯}{m}Ft}},{{\gamma \left( {t - \tau_{p} - {nT}} \right)}e^{j2{\pi {({{m\; F} + \upsilon_{d}})}}t}}}\rangle} = {{\langle{{g\left( {t - {\overset{¯}{n}T}} \right)},{{\gamma \left( {t - {nT} - \tau_{p}} \right)}e^{j2{\pi {({{{\lbrack{m - \overset{¯}{m}}\rbrack}F} + \upsilon_{d}})}}t}}}\rangle} = {{\langle{{g\left( \overset{¯}{t} \right)},{{\gamma \left( {\overset{¯}{t} - {\left\lbrack {n - \overset{¯}{n}} \right\rbrack T} - \tau_{p}} \right)}e^{j2{{\pi {({{{\lbrack{m - \overset{¯}{m}}\rbrack}F} + \upsilon_{d}})}}{\lbrack{\overset{¯}{t} + {\overset{¯}{n}T}}\rbrack}}}}}\rangle} = {{e^{j2{\pi {({{{\lbrack{m - \overset{¯}{m}}\rbrack}F} + \upsilon_{d}})}}\overset{¯}{n}T} \times {\langle{{g\left( \overset{¯}{t} \right)},\ {{\gamma \left( {\overset{¯}{t} - {\left\lbrack {n - \overset{¯}{n}} \right\rbrack T} - \tau_{p}} \right)}e^{j2{\pi {({{{\lbrack{m - \overset{¯}{m}}\rbrack}F} + \upsilon_{d}})}}\overset{¯}{t}}}}\rangle}} = {e^{j2{\pi {({{{\lbrack{m - \overset{¯}{m}}\rbrack}F} + \upsilon_{d}})}}\overset{¯}{n}T}\  \cdot {A\left( {{{\left\lbrack {n - \overset{¯}{n}} \right\rbrack T} + \tau_{p}},\ {{\left\lbrack {m - \overset{¯}{m}} \right\rbrack F} + \upsilon_{d}}} \right)}}}}}$

where A(τ,ν)=Ag, γ(τ, ν)=

g(t), γ(t−τ)e^(i2πνt)

is the cross-ambiguity function. With matched pulse shaping one wishesto “approach”:

A([n−n ]T+τ _(p) p,[m−m ]F+v _(d))≈δ(n−n )δ(m−m )A(τ_(p),ν_(d))  (15)

for all values (τ_(p),ν_(d))∈U, where U is the set of time-frequencyshifts, and where |U|≠0. On a informal level, this would mean that theexpected power

(|I _(m n) |²) (taken over data symbols and channel realizations) of theself-interference term I _(m n) , which may be defined as:

$\begin{matrix}{I_{\overset{\_}{m}\; \overset{\_}{n}} = {\sum\limits_{{({mn})} \neq {({\overset{\_}{m},\overset{¯}{n}})}}{x_{mn}S_{dp}e^{{- 2}\; {\pi {({{\overset{\_}{m}\; F\; \tau_{p}} - {\overset{\_}{n}T\; \upsilon_{d}} - {{\lbrack{m - \overset{\_}{m}}\rbrack}F\; \overset{\_}{n}\; T}})}}}{A\left( {{{\left\lbrack {n - \overset{\_}{n}} \right\rbrack T} + {\tau_{p}p}},{{\left\lbrack {m - \overset{\_}{m}} \right\rbrack F} + \upsilon_{d}}} \right)}}}} & (16)\end{matrix}$

may vanish (i.e. become small). However, since such “idealized” pulses gand γ such that A_(gγ)(τ,ν)˜δ(τ)δ(ν) for all the (τ,ν) in considerationabove might not exist,

(|I _(m n) |²) may always be non-zero. The idea of matched pulse shapingis then to control expected self-interference power. Thus,self-interference I _(m n) may be considered in the system modelexplicitly, yielding:

$\begin{matrix}{y_{\overset{\_}{m}\; \overset{¯}{n}} = {{x_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}{\sum\limits_{{({d,p})} \in A}{{\overset{\hat{}}{S}}_{dp}e^{{- j}2{\pi {({{\overset{\_}{m}\; F\; \tau_{p}} - {\overset{\_}{n}\; T\; \upsilon_{d}}})}}}}}} + I_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}}} & (17)\end{matrix}$

where

${\Sigma_{{({d,p})} \in A}{\hat{S}}_{dp}e^{{- j}2{\pi {({{\overset{\_}{m}\; F\; \tau_{p}} - {\overset{¯}{n}T\; \upsilon_{d}}})}}}} = h_{\overset{\_}{m}\mspace{11mu} \overset{\_}{n}}$

(the channel) and where the vector Ŝ may be defined with componentsŜ_(dp)=S_(dp)·A(τ_(p),v_(d)).

Applying F_(s) to (17) may indicate that in the first order (up toinference) the channel acts as 2D convolution since:

$\begin{matrix}{Y_{\overset{\_}{lk}} = {{\sum\limits_{{({\overset{\_}{m}\overset{¯}{n}})} \in I}{y_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}e^{{- j}\; 2\; {\pi {({\frac{\overset{\_}{n}\; \overset{\_}{k}}{N} - \frac{\overset{\_}{m}\overset{\_}{l}}{M}})}}}}} = {{\sum\limits_{{({\overset{\_}{m}\mspace{11mu} \overset{¯}{n}})} \in I}{\left( {{h_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}x_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}} + I_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}} \right)e^{{- j}\; 2\; {\pi {({\frac{\overset{\_}{n}\; \overset{\_}{k}}{N} - \frac{\overset{\_}{m}\overset{\_}{l}}{M}})}}}}} = {{\sum\limits_{{({\overset{\_}{m}\mspace{11mu} \overset{¯}{n}})} \in I}{\left( {h_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}x_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}} \right)e^{{- j}2{\pi {({\frac{\overset{\_}{n}\; \overset{\_}{k}}{N} - \frac{\overset{\_}{m}\overset{\_}{l}}{M}})}}}}} + I_{\overset{\_}{l}\; \overset{\_}{k}}}}}} & (18)\end{matrix}$

and pointwise multiplication in the time-frequency plane is (circular)2D-convolution in the delay-Doppler plane:

Y _(l k) =(H*X) _(l k) +I _(l k)   (19)

Embodiments may provide a delay-Doppler channel estimation. The channelwith the pilot sent by the transmitter in the DD domain may beestimated. For this, the F_(s) ⁻¹ may be applied to half of the guardarea, where the channel impulse response (CIR) is obtained (see e.g. P.Raviteja, K. et al: “Embedded pilot-aided channel estimation for OTFS indelay-Doppler channels”):

$\begin{matrix}{{{\hat{h}}_{\overset{\_}{m}\mspace{11mu} \overset{\_}{n}}{\sum\limits_{{\overset{¯}{l} = 1},{\overset{¯}{k} = {N - Q}}}^{{\overset{¯}{l} = W},{\overset{¯}{k} = {2Q}}}{\left( {H*X} \right)_{\overset{\_}{l\; k}}e^{j2{\pi {({\frac{\overset{\_}{n}\; \overset{\_}{k}}{N} - \frac{\overset{\_}{m}\overset{\_}{l}}{M}})}}}}}} + I_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}} & (20)\end{matrix}$

for all (m, n)∈I. FIG. 1 highlights the symbols used for channelestimation in a black dashed frames (i.e. the pilot symbol 110 and asubset of the guard symbols 120).

At least some embodiments include Time-Frequency Equalization. In someconcepts, computational feasible equalizers may suffer from mismatchedtime-frequency grids. Parity may be achieved with perfect gird matchingand pulse-shaping of the Gabor synthesis and analysis pulses with thedelay and Doppler spread of the channel. By introducing grid matching,the equalization performance may be improved and hence a higher OTFSdiversity may be achieved. However, evaluations have shown that thecross terms may be compensated further, not only by grid matching, inorder to improve the performance.

For channel equalization, linear equalizers may be favored due to theirlower complexity compared to maximum likelihood estimation (MLE)equalizers. Although MLE enjoy an increased diversity, in some casesalso linear equalizer can achieve the same diversity gain as MLE, forexample in the case of non-singular convolutions. However, in T. Zemenet al: “Low-complexity equalization for orthogonal time and frequencysignaling (OTFS)” it has been observed that in general, full OTFSdiversity is not obtained when using common minimum mean square error(MMSE) equalization in the TF domain and then MLE decoding is required.On the other hand, MLE or interference cancellation techniques for OTFSmay be complex and require also accurate estimation of the crosstalkchannel coefficients.

In order to obtain sufficient performance at moderate complexity for apractical implementation, at least some embodiments may use mobilitymodes which control the self-interference on a coarse level, and use theMMSE equalization to account for the remaining self-interference power.In detail, the received frame (17) may be equalized by a MMSEequalization in TF domain with estimated channel obtained in (20):

$\begin{matrix}{{\overset{\hat{}}{X}}_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}} = {y_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}\frac{{\overset{\hat{}}{h}}_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}^{*}}{\left| {\overset{\hat{}}{h}}_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}} \middle| {}_{2}{{+ \sigma^{2}} + {_{x}\left\{ \left| I_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}} \middle| {}_{2}{+ \left| {h_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}} - {\overset{\hat{}}{h}}_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}} \right|^{2}} \right. \right\}}} \right.}}} & \left( {21} \right)\end{matrix}$

where σ² is the squared standard deviation of the noise at the receiver.For example, I may be defined by I=Σ _(m n≠mn)|h_(mn)|².

To estimate the expectation above, the empirical mean for the power ofthe self-interference and estimation error in a calibration phase may bedetermined. This deterministic value may be used for the numericalresults of FIGS. 3a, 3b, and 4a to 4d . Finally, the equalized frame maybe received with (5) in the DD domain.

$\begin{matrix}{{\overset{\hat{}}{X}}_{\overset{\_}{lk}} = {\sum\limits_{{({\overset{\_}{m}\mspace{11mu} \overset{¯}{n}})} \in I}{{\overset{\hat{}}{x}}_{\overset{\_}{m}\mspace{11mu} \overset{¯}{n}}e^{{- j}2{\pi {({\frac{\overset{\_}{n}\; \overset{\_}{k}}{N} - \frac{\overset{\_}{m}\overset{\_}{l}}{M}})}}}}}} & (22)\end{matrix}$

In order to obtain the same diversity gain as MLE, at least someembodiments may extend the common MMSE equalizer by a term to compensatethe self-interference caused by the channel cross terms. Therefore, thecross-term interference (i.e. the self-interference) may be determinedat the receiver (i.e. by the processing module) using the receivedpilot, and the compensation term may be determined in the delay-Dopplerdomain based on the knowledge of the pilot(s) and guard symbols. Inother words, the processing module 24 may be configured to performequalization on received data frames. Accordingly, the method maycomprise performing 260 equalization on received data frames. Theequalization may be performed using a minimum mean square equalizer (seee.g. equation 21). The minimum mean square equalizer may comprise a termto compensate for self-interference (e.g. |I _(m n) |² or I _(m n) ofequation 21). At the receiver it an a priori knowledge of the pilot setX _(k l) and the squared standard deviation of the receiver noise may beused to calculate the term to compensate for the self-interference. Theterm to compensate for the self-interference may be calculated byL2-norm minimization of the error (or of another norm). For example, theterm to compensate for the self-interference (e.g. for use in equation21) may be calculated using:

$I_{l\; 2} = {\arg_{I}\min {\sum\limits_{{({\overset{\_}{k},\overset{\_}{l}})} \in P}{{{{\hat{X}}_{\overset{\_}{l}\; \overset{\_}{k}}(I)} - X_{\overset{\_}{l}\; \overset{\_}{k}}}}^{2}}}$

where I for the lowest term is obtained using L2-norm minimization. Inother words, the above equation may be calculated over a range of valuesfor I (and the corresponding equalized received signal in delay-Dopplerrepresentation, Ŷ _(k l) ) in order to obtain the value for which theself-interference is suppressed. For example, equation 21 may be used tocalculate the values ofŶ_({circumflex over (k)}{circumflex over (l)})(I). Furthermore, thiscompensation factor may be estimated (by choosing adequate values of I,for which the minimization is performed, and it may be predicted for thefuture in order to accelerate and simply the process.

In other words, the processing module 24 may be configured to determinethe term to compensate for self-interference using a previously receiveddata frame. Accordingly, the method may comprise determining 262 theterm to compensate for self-interference using a previously receiveddata frame. For example, as pointed out above, a range of differentvalues for the term to compensate for self-interference may be tried onthe previously received data frame, and the term to compensate forself-interference may be chosen based on the value that has performedbest (e.g. as indicated by the result of the equalization). This may bedone based on the guard symbols and pilot in the delay-Doppler plane.For example, the term to compensate for self-interference may bedetermined using a subset of the plurality of guard symbols, andoptionally the pilot symbol, of the previously received data frame. Inother words, the processing module 24 may be configured to determine theterm to compensate self-interference by performing the equalizationusing a plurality of values for the term to compensate forself-interference, evaluating a quality of a result of the equalizationperformed using the plurality of values (e.g. a deviation of the sum ofthe values obtained for the guard symbols from zero), and selecting avalue of the plurality of values for the term to compensate forself-interference based on the evaluation (e.g. by picking the term tocompensate for self-interference that yields the lowest sum of thevalues obtained for the guard symbols). For example, as shownpreviously, the SFFT might be performed (only) for the guard and pilotsymbols in the delay-Doppler plane. If the guard symbols are assumed toyield zero (if the self-interference is corrected for), the deviationfrom zero may be used as minimization criterion. Accordingly, the termto compensate self-interference may be determined 262 by performing 260the equalization using a plurality of values for the term to compensatefor self-interference, evaluating 264 a quality of a result of theequalization performed using the plurality of values, and selecting 266a value of the plurality of values for the term to compensate forself-interference based on the evaluation.

In more detail, the two-dimensional time-frequency grid may be derivedfrom a two-dimensional grid in a delay-Doppler plane having a delaydimension and a Doppler dimension. The processing module 24 may beconfigured to perform a symplectic Fourier transform on the receiveddata frame (e.g. based on the equalized data frame that was equalizedusing a value of a range of values for the term to compensate for theself-interference). Accordingly, the method may comprise performing 234a symplectic Fourier transform on the received data frame. Thesymplectic Fourier transform may be performed (only) for the points onthe two-dimensional grid in the delay-Doppler plane corresponding to thesubset of the plurality of guard symbols (and optionally for the pointon the two-dimensional grid in the delay-Doppler plane corresponding tothe pilot symbol). The processing module may be configured to determinethe term to compensate for self-interference based on a result of thesymplectic Fourier transform. Accordingly, the method may comprisedetermining 262 the term to compensate for self-interference based on aresult of the symplectic Fourier transform. For example, the result ofthe SFFT may be used for the evaluation of the quality of the result ofthe equalization. In other words, the result of the SFFT may show thequality of the term to compensate for the self-interference.

The calculation of this compensation factor (i.e. of the term tocompensate for self-interference) does not necessarily be calculated forevery frame. It might be enough to update it after several frames. Inother words, the processing module 24 may be configured to periodicallyupdate the term to compensate for the self-interference. Accordingly,the method may comprise periodically updating 268 the term to compensatefor the self-interference. For example, the term to compensate for theself-interference might be updated at most every second (or every third,every fourth, every nth) data frame. Alternatively, the term tocompensate for the self-interference might be updated if the quality ofthe equalization deteriorates (too much). For example, the processingmodule 24 may be configured to update the term to compensate for theself-interference if a bit-error rate of a received data frame exceeds athreshold. Accordingly, the method may comprise updating 268 the term tocompensate for the self-interference if a bit-error rate of a receiveddata frame exceeds a threshold.

Furthermore, the compensation term might be sent back to thetransmitter. For example, the processing module 24 may be configured totransmit information about the term to compensate for self-interferenceto the further wireless communication device. Accordingly, the methodmay comprise transmitting 269 information about the term to compensatefor self-interference to the further wireless communication device. Forexample, the information about the term to compensate forself-interference may comprise a numerical value of the term tocompensate for self-interference, or one or more component values thatcan be used to calculate the term to compensate for self-interference atthe further wireless communication device.

The transceiver module 22 may be implemented as any means fortransceiving, i.e. receiving and/or transmitting etc., one or moretransceiver units, one or more transceiver devices and it may comprisetypical receiver and/or transmitter components, such as one or moreelements of the group of one or more Low-Noise Amplifiers (LNAs), one ormore Power Amplifiers (PAs), one or more filters or filter circuitry,one or more diplexers, one or more duplexers, one or moreAnalog-to-Digital converters (A/D), one or more Digital-to-Analogconverters (D/A), one or more modulators or demodulators, one or moremixers, one or more antennas, etc. In some embodiments, the processingmodule 24 may provide some functionality that may be found intransceiver modules. For example, the processing module 24 may be aprocessing module of the transceiver module 22, and may comprise one ormore filters or filter circuitry and/or one or more modulators ordemodulators.

In embodiments the processing module 24 may be implemented using one ormore processing units, one or more processing devices, any means forprocessing, such as a processor, a computer or a programmable hardwarecomponent being operable with accordingly adapted software. In otherwords, the described function of the processing module 24 may as well beimplemented in software, which is then executed on one or moreprogrammable hardware components. Such hardware components may comprisea general purpose processor, a Digital Signal Processor (DSP), amicro-controller, etc.

In the following, an evaluation of the mobility modes is shown withnumerical results of different configurations. The approach of usingdistinct mobility modes for grid and pulse matching may be shown. Thegoal of these mobility modes may be to approach a good approximation(small deviation from equality) in (15) and hence to reduce theself-interference. This may be fulfilled when all system parameters suchas the grid and pulses match the delay and Doppler spread of the channelas stated in (1). In order to cope with different channel conditions,i.e. distinct delay and Doppler spreads, five mobility modes areinvestigated. The mobility modes may be chosen according to a scheme, inwhich the higher the resolution in time (N symbols) the less resolutionin frequency domain (M subcarrier) may be available and vice versa. ModeI of FIG. 3a (64 points in all dimensions) represents the case for equaltime and frequency resolution. It may be referred to a G-Mode or R-Mode,when at the Gabor filter bank a Gaussian or rectangular pulse is used,respectively.

FIGS. 3a and 3b show these mobility modes and indicate at which SNR(Signal-to-Noise-Ratio) level a certain BER (Bit Error Ratio) thresholdis exceeded. FIG. 3a shows a required SNR to exceed the threshold ofBER=10⁻² for mobility modes I-V, FIG. 3b shows a required SNR to exceedthe threshold of BER=10⁻³ for mobility modes I-V. These thresholds canbe used to trigger channel coding. For the evaluation of BER curves, twothresholds may be considered. First, in FIG. 3a , the SNR needed toexceed a BER threshold of 10⁻² bits is shown. Second, in FIG. 3b , therequired SNR fora lower BER threshold of 10⁻³ bits is explored. FIGS. 3aand 3b therefore depict the first and second BER threshold,respectively. In FIGS. 3a and 3b , the SNR required to exceed the BERthreshold is shown for three scenario: vehicle-to-infrastructure (V2I)at 10 km/h (reference sign 310), V2I at 190 km/h (reference sign 320)and vehicle-to-vehicle (V2V) at 200 km/h (reference sign 330). Thevalues are shown for five modes (I-V) and rectangular and Gaussianpulses. Mobility mode I has an N of 64 and an M of 64 (N being thenumber of symbols, i.e. the number of points in the time dimension ofthe time-frequency plane, M being the number of sub-carriers, i.e. thenumber of points in the frequency dimension of the time-frequencyplane). Mobility mode II has an N of 256 and an M of 16. Mobility modeIII has an N of 16 and an M of 256. Mobility mode IV has an N of 1024and an M of 4. Mobility mode V has an N of 4 and an M of 1024. As shownin FIG. 3a , to achieve a BET of 10⁻², the best results for V2I at 10km/h (310) was found with mobility mode III and a Gaussian pulse (10.6dB), the best result for V2I at 190 km/h (320) was found with mobilitymode I and a Gaussian pulse (8.8 dB), and the best result for V2V at 200km/h (330) was found with either mobility mode I or II and a Gaussianpulse (7.7 dB). As shown in FIG. 3b , to achieve a BET of 10⁻³, the bestresults for V2I at 10 km/h (310) was found with mobility mode V and aGaussian pulse (18.1 dB), and the best result for V2V at 200 km/h (330)was found with mobility mode II and a Gaussian pulse (12.9 dB). FIG. 3csummarizes the parameters used to obtain the numerical results.

FIGS. 4a to 4d show BER curves for three distinct vehicular channels fordifferent mobility modes. The mobility modes I to V (of FIGS. 3a and 3b) are referenced by reference signs G-Mode I (mobility mode I, Gaussianpulse), R-Mode I (mobility mode I, rectangular pulse), G-Mode II(mobility mode II, Gaussian pulse) etc. FIG. 4a depicts avehicle-to-infrastructure (V2I) channel for lower velocities (10 km/h,reference sign 310). Mode IV and II are not exceeding any BER threshold.Mode III reaches the first BER threshold before the remaining modes. Forthe lower threshold Mode V outperforms the other modes and also reachesthe lowest error floor.

In FIG. 4b , a V2I channel for higher velocities is plotted, where ModeIV and V are not exceeding any BER threshold. Note that Mode V performsgood for low but not for the high velocity V2I channel (190 km/h,reference sign 320). The best performance is achieved with Mode I, whereBER threshold is reached for a SNR of 8.8 dB (see FIG. 3a ). The secondBER threshold is not reached by any mode, as depicted in FIG. 3 b.

The V2V channel is evaluated as third communication link. FIG. 4cdepicts a high speed V2V channel with a relative velocity of 200^(km)/h(reference sign 330). Here both Mode I and II outperform the othermobility modes and exceed the first BER threshold for a SNR of 7.7 dB(see FIG. 3a ). The second BER threshold is reached first by Mode II,which is offering the lowest error floor.

In FIG. 4d , Mode II is depicted in comparison to an ideal channelestimation (V2V, relative velocity of 200^(km)/h, reference sign 330).It can be observed, that even if the best mobility mode is selected,there is still self-interference and an estimation error which might becompensated with a more advanced channel estimation and equalization.

OTFS modulation was introduced from the classical viewpoint of a pulseshaped multicarrier scheme, also called Weyl Heisenberg or Gaborsignaling, with additional spreading using the symplectic Fouriertransform. Selecting an appropriate mobility mode for pulse and gridmatching the self-interference level, immanent in doubly-dispersivechannels, may reduce and hence also the operation point to support atarget BER threshold required for certain types of channel coding. Itmay be concluded that through the introduction of mobility modes, thesystem performance for low-complexity equalizers implementing tuned2D-deconvolutions may be improved instead of dealing with the fulltwisted convolution. For each vehicular channel a distinct mobility modemay outperform the other modes and the effect may improve with moreaccurate channel knowledge. Tuning the equalizer for instantaneousinterference levels may provide further gains of mobility modes.

The aspects and features mentioned and described together with one ormore of the previously detailed examples and figures, may as well becombined with one or more of the other examples in order to replace alike feature of the other example or in order to additionally introducethe feature to the other example.

Examples may further be or relate to a computer program having a programcode for performing one or more of the above methods, when the computerprogram is executed on a computer or processor. Steps, operations orprocesses of various above-described methods may be performed byprogrammed computers or processors. Examples may also cover programstorage devices such as digital data storage media, which are machine,processor or computer readable and encode machine-executable,processor-executable or computer-executable programs of instructions.The instructions perform or cause performing some or all of the acts ofthe above-described methods. The program storage devices may comprise orbe, for instance, digital memories, magnetic storage media such asmagnetic disks and magnetic tapes, hard drives, or optically readabledigital data storage media. Further examples may also cover computers,processors or control units programmed to perform the acts of theabove-described methods or (field) programmable logic arrays ((F)PLAs)or (field) programmable gate arrays ((F)PGAs), programmed to perform theacts of the above-described methods.

The description and drawings merely illustrate the principles of thedisclosure. Furthermore, all examples recited herein are principallyintended expressly to be only for illustrative purposes to aid thereader in understanding the principles of the disclosure and theconcepts contributed by the inventor(s) to furthering the art. Allstatements herein reciting principles, aspects, and examples of thedisclosure, as well as specific examples thereof, are intended toencompass equivalents thereof.

A functional block denoted as “means for . . . ” performing a certainfunction may refer to a circuit that is configured to perform a certainfunction. Hence, a “means for s.th.” may be implemented as a “meansconfigured to or suited for s.th.”, such as a device or a circuitconfigured to or suited for the respective task.

Functions of various elements shown in the figures, including anyfunctional blocks labeled as “means”, “means for providing a signal”,“means for generating a signal.”, etc., may be implemented in the formof dedicated hardware, such as “a signal provider”, “a signal processingunit”, “a processor”, “a controller”, etc. as well as hardware capableof executing software in association with appropriate software. Whenprovided by a processor, the functions may be provided by a singlededicated processor, by a single shared processor, or by a plurality ofindividual processors, some of which or all of which may be shared.However, the term “processor” or “controller” is by far not limited tohardware exclusively capable of executing software, but may includedigital signal processor (DSP) hardware, network processor, applicationspecific integrated circuit (ASIC), field programmable gate array(FPGA), read only memory (ROM) for storing software, random accessmemory (RAM), and non-volatile storage. Other hardware, conventionaland/or custom, may also be included.

A block diagram may, for instance, illustrate a high-level circuitdiagram implementing the principles of the disclosure. Similarly, a flowchart, a flow diagram, a state transition diagram, a pseudo code, andthe like may represent various processes, operations or steps, whichmay, for instance, be substantially represented in computer readablemedium and so executed by a computer or processor, whether or not suchcomputer or processor is explicitly shown. Methods disclosed in thespecification or in the claims may be implemented by a device havingmeans for performing each of the respective acts of these methods.

It is to be understood that the disclosure of multiple acts, processes,operations, steps or functions disclosed in the specification or claimsmay not be construed as to be within the specific order, unlessexplicitly or implicitly stated otherwise, for instance for technicalreasons. Therefore, the disclosure of multiple acts or functions willnot limit these to a particular order unless such acts or functions arenot interchangeable for technical reasons. Furthermore, in some examplesa single act, function, process, operation or step may include or may bebroken into multiple sub-acts, -functions, -processes, -operations or-steps, respectively. Such sub acts may be included and part of thedisclosure of this single act unless explicitly excluded.

Furthermore, the following claims are hereby incorporated into thedetailed description, where each claim may stand on its own as aseparate example. While each claim may stand on its own as a separateexample, it is to be noted that—although a dependent claim may refer inthe claims to a specific combination with one or more other claims—otherexamples may also include a combination of the dependent claim with thesubject matter of each other dependent or independent claim. Suchcombinations are explicitly proposed herein unless it is stated that aspecific combination is not intended. Furthermore, it is intended toinclude also features of a claim to any other independent claim even ifthis claim is not directly made dependent to the independent claim.

What is claimed is:
 1. An apparatus for a wireless communication device,the apparatus comprising: a transceiver module for transmitting andreceiving wireless transmissions; and a processing module configured to:control the transceiver module, communicate with a further wirelesscommunication device via the transceiver module, wherein thecommunication with the further wireless communication device is based ona transmission of data frames between the wireless communication deviceand the further wireless communication device, wherein each data frameis based on a two-dimensional grid in a time-frequency plane having atime dimension resolution and a frequency dimension resolution, whereinthe two-dimensional time-frequency grid is derived from atwo-dimensional grid in a delay-Doppler plane having a delay dimensionand a Doppler dimension, wherein the processing module is configured toperform equalization on received data frames, wherein the equalizationis performed using a minimum mean square equalizer, the minimum meansquare equalizer comprising a term to compensate for self-interference.2. The apparatus according to claim 1, wherein the processing module isconfigured to determine the term to compensate for self-interferenceusing a previously received data frame.
 3. The apparatus according toclaim 2, wherein the processing module is configured to determine theterm to compensate self-interference by performing the equalizationusing a plurality of values for the term to compensate forself-interference, evaluating a quality of a result of the equalizationperformed using the plurality of values, and selecting a value of theplurality of values for the term to compensate for self-interferencebased on the evaluation.
 4. The apparatus according to claim 1, whereineach data frame comprises a pilot symbol and a plurality of guardsymbols surrounding the pilot symbol, wherein the processing module isconfigured to determine the term to compensate for self-interferenceusing the pilot symbol and a subset of the plurality of guard symbols ofthe previously received data frame.
 5. The apparatus according to claim4, wherein the two-dimensional time-frequency grid is derived from atwo-dimensional grid in a delay-Doppler plane having a delay dimensionand a Doppler dimension, wherein the processing module is configured toperform an inverse symplectic Fourier transform on the received dataframe, wherein the inverse symplectic Fourier transform is performed forthe points on the two-dimensional grid in the delay-Doppler planecorresponding to the pilot symbol and to the subset of the plurality ofguard symbols, and to determine the term to compensate forself-interference based on a result of the inverse symplectic Fouriertransform.
 6. The apparatus according to claim 1, wherein the processingmodule is configured to periodically update the term to compensate forthe self-interference.
 7. The apparatus according to claim 1, whereinthe processing module is configured to update the term to compensate forthe self-interference if a bit-error rate of a received data frameexceeds a threshold.
 8. The apparatus according to claim 1, wherein theprocessing module is configured to transmit information about the termto compensate for self-interference to the further wirelesscommunication device.
 9. The apparatus according to claim 1, wherein theprocessing module is configured to select a communication mode from aplurality of communication modes for the communication between thewireless communication device and the wireless communication device,wherein the communication mode defines a combination of a frequencydimension resolution and a time dimension resolution of thetwo-dimensional grid in the time-frequency plane.
 10. The apparatusaccording to claim 9, wherein the processing module is configured toselect the communication mode from the plurality of communication modesbased on an estimated self-interference of the plurality ofcommunication modes.
 11. The apparatus according to claim 1, wherein thedata frame is an Orthogonal Time-Frequency Spreading data frame.
 12. Awireless communication device comprising the apparatus according toclaim
 1. 13. A method for a wireless communication device, the methodcomprising: communicating with a further wireless communication devicevia the transceiver module, wherein the communication with the furtherwireless communication device is based on a transmission of data framesbetween the wireless communication device and the further wirelesscommunication device, wherein each data frame is based on atwo-dimensional grid in a time-frequency plane having a time dimensionresolution and a frequency dimension resolution, wherein thetwo-dimensional time-frequency grid is derived from a two-dimensionalgrid in a delay-Doppler plane having a delay dimension and a Dopplerdimension; and Performing equalization on received data frames, whereinthe equalization is performed using a minimum mean square equalizer, theminimum mean square equalizer comprising a term to compensate forself-interference.
 14. The method according to claim 13, wherein themethod comprises selecting a communication mode from a plurality ofcommunication modes for the communication between the wirelesscommunication device and the wireless communication device, wherein thecommunication mode defines a combination of a frequency dimensionresolution and a time dimension resolution of the two-dimensional gridin the time-frequency plane.
 15. A computer program having a programcode for performing a method for a wireless communication device, whenthe computer program is executed on a computer, a processor, or aprogrammable hardware component, the method comprising: communicatingwith a further wireless communication device via the transceiver module,wherein the communication with the further wireless communication deviceis based on a transmission of data frames between the wirelesscommunication device and the further wireless communication device,wherein each data frame is based on a two-dimensional grid in atime-frequency plane having a time dimension resolution and a frequencydimension resolution, wherein the two-dimensional time-frequency grid isderived from a two-dimensional grid in a delay-Doppler plane having adelay dimension and a Doppler dimension; and Performing equalization onreceived data frames, wherein the equalization is performed using aminimum mean square equalizer, the minimum mean square equalizercomprising a term to compensate for self-interference.